Light a hardwood charcoal fire. Brush the asparagus with olive oil and season with salt and pepper. Grill the asparagus over moderately high heat, turning, until lightly charred and almost tender, 4 minutes. Transfer to a plate and let cool.

Meanwhile, in a small cast-iron skillet, heat the 1 tablespoon of olive oil. Add the bread crumbs and garlic and cook over moderately high heat, stirring, until the crumbs are golden and crisp, 4 minutes. Remove from the heat and let cool slightly, then stir in the Parmigiano-Reggiano, parsley and lemon zest; season with salt and pepper.

Divide the asparagus into 6 even piles. On a work surface, arrange the prosciutto slices in 6 pairs, overlapping slightly. Set an asparagus pile on each prosciutto pair and roll up.

Grill the bundles over moderately high heat, turning, until the asparagus are tender and the prosciutto is crisp, 4 minutes. Transfer to a platter. Sprinkle the lemony bread crumbs on top and serve.